A manufacturer produces cherry, peppermint, cinnamon, and orange-flavored gum. Each flavor is available with sugar or sugar-free. The gum

is sold in 2 ounce, 4-ounce, or 8 ounce packages,

How many different types of labels will the manufacturers have to produce?

Answer:

this triangle is ABC with A(-2 ; -3), B(4; - 3) and C(3;5)

=> [tex]AB=\sqrt{(4-(-2))^{2}+\sqrt{(-3 -(-3))^{2} } }=\sqrt{6^{2} }=6\\\\AC=\sqrt{(3-(-2))^{2}+(5-(-3))^{2} }=\sqrt{5^{2}+8^{2} }=\sqrt{89}\\\\BC =\sqrt{1^{2}+8^{2} }=\sqrt{65}[/tex]

using Heron theorem, we have:

[tex]S=\sqrt{p(p-AB)(p-AC)(p-BC)}\\\\S=\sqrt{(\frac{6+\sqrt{89}+\sqrt{65} }{2})(\frac{\sqrt{89}+\sqrt{65}-6 }{2} )(\frac{6+\sqrt{65}-\sqrt{89} }{2})(\frac{6+\sqrt{89}-\sqrt{65} }{2}) }\\\\S=24 \\\\[/tex]

with S is the area of the triangle

       [tex]p=\frac{AB+AC+BC}{2}=\frac{6+\sqrt{89}+\sqrt{65} }{2}[/tex]

Step-by-step explanation:

Area of the triangle with given vertices is equals to 24 square units.

"Area is the surface which represents the total space occupied by any two dimensional object."

"Triangle is a  polygon which has three sides and three vertices. Sum of all the interior angles of a triangle is equals to 180°."

Formula used

In ΔABC , A(x₁ , y₁) , B(x₂, y₂) and C(x₃, y₃)

Area of a triangle =  [tex]\frac{1}{2} [ x_{1} (y_{2} -y_{3} + x_{2} (y_{3} -y_{1} +x_{3} (y_{1} -y_{2} ]\\[/tex]

According to the question,

Let ABC be the triangle with A(-2,-3) , B(4,-3) and C(3,5)

Area of the triangle = [tex]\frac{1}{2}[/tex] [ -2(-3-5) + 4(5+3) +3 (-3 +3)]

                                 = [tex]\frac{1}{2}[/tex] [ 16 +32 + 0]

                                 = 24 square units

Hence Area of the triangle with given vertices is equals to 24 square units.

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Answer:

Step-by-step explanation:

Taking the determinant of the matrices we will have;

= 4x(5y) - 2x(3y)

= 20xy - 6xy

= 14xy

Given x = -2 and y = 3

Determinant = 14(-2)(3)

Determinant = -28*3

Determinant = -84

Answer:

i believe 1-3-5

Step-by-step explanation:

Answer: the 2nd and 6th

Step-by-step explanation:

i did the test thing

Answer: y = 5/2x - 4

Step-by-step explanation:

the equation is y = ax + b (a ≠ 0)

because the slope of the line is 5/2 => a = 5/2

               the line passes through (0; -4) => -4 = b

=> the equation is y = 5/2.x - 4

Given:

The area of the rectangle RSTU = [tex]36x^2+25x-25[/tex]

Length of the rectangle RSTU = [tex]4x+5[/tex]

To find:

The width of the rectangle RSTU.

Step-by-step explanation:

We have,

[tex]36x^2+25x-25[/tex]

Splitting the middle term, we get

[tex]=36x^2+45x-20x-25[/tex]

[tex]=9x(4x+5)-5(4x+5)[/tex]

[tex]=(4x+5)(9x-5)[/tex]

We know that, the area of a rectangle is

[tex]Area=Length \times width[/tex]

Area of rectangle is product of (4x+5) and (9x-5).

Since (4x+5) is the length of the rectangle, therefore, (9x-5) is the width of the rectangle RSTU.

Answer:

Perimeter = 65.12 in

Area = 292.48 in^2

which agrees with the second answer choice

Step-by-step explanation:

The perimeter is going to be the addition of the sides of the rectangle external to the composite figure ( 12 + 16 + 12 = 40) PLUS the length of half of the circumference or radius 8 inches  (which is pi * radius = 3.14 * 8 = 25.12 in)

Then the total perimeter is:

Perimeter = 40 in + 25.12 in = 65.12 in

The are is going to be the area of the rectangle (12 * 16 = 192 square inches) PLUS the area of the semicircle of radius 8 in (pi *radius^2 /2 = 100.48 square inches).

Therefore the total area is:

Area = 192 + 100.48  = 292.48 in^2

Answer:

Both are 77

Step-by-step explanation:

103 + 103 = 206

360 - 206 = 154

154/2 = 77

Answer:

10x/3

Step-by-step explanation:

10x/3.............................

Answer:

Attached please find answer

Step-by-step explanation:

= (x² + x - 42) / (x - 6)

= [x² + (7x - 6x) - 42] / (x - 6)

= [x² + 7x - 6x - 42] / (x - 6)

= [(x² + 7x) - (6x + 42)] / (x - 6)

= [x(x + 7) - 6(x + 7)] / (x - 6)

= [(x + 7)(x - 6)] / (x - 6)

= x + 7 → when x approches 6

= 6 + 7

= 13

Other method:

Lim   (x² + x - 42) / (x - 6)

x→ 6

When x → 6, there is an indeterminate expression because: 6 - 6 = 0

Do you know the l'Hôpital's rule, when x → a:

Lim [ f(x) / g(x) ] = Lim [ f'(x) / g'(x) ]

f(x) = x² + x - 42

f'(x) = 2x + 1

g(x) = x - 6

g'(x) = 1

= f'(x) / g'(x)

= (2x + 1)/1

= 2x + 1 → when x approches 6

= 12 + 1

= 13

Anwser: First triangle area =0.5*8*10=40 in2. Secound triangle area =0.5*8*6=24 in2 Sum is 1st area + 2nd area, which is 64 in2.

Answer:

38 students chose to fly

Step-by-step explanation:

add the female and male

Answer:

7 or 8 miles per hour

Step-by-step explanation:

The rate of current or velocity of current upriver is 4.5 miles per hour.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.

Let's suppose the velocity or speed of the boat (Velocity in still water ) = V miles/hour

Velocity of current = x miles/hour

Given that,

The boat takes 2 hours to travel 15 miles upriver against the current.

15 miles  in 2 hour

⇒ 7.5 miles/hour

Since it is traveling against the current velocity so

V  - x = 7.5

And V = 12 miles/hour

By substitution,

12 - x = 7.5

x = 12 - 7.5

x = 4.5 miles/hour

Hence "The rate of current or velocity of current upriver is 4.5 miles per hour".

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Answer:

y=20x+10

Step-by-step explanation:

You start with $10, so this will be added on, and is not affected by the number of months.

You add $20 each month, so the 20 is dependant on x.

ANSWER: y=20x+10

Answer:

2

Step-by-step explanation:

1 2/3     5/6

5/3 -> 10/6 -> 3 1/3

1 2/3 x 2 = 3 1/3

There are [tex]\frac{1}{2}[/tex] groups of the first fraction in the second fraction.

Given the following data:

A fraction is a numerical quantity that is not expressed as a whole number. Therefore, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include:

Next, we would divide the second fraction by the first fraction as follows:

[tex]Groups = \frac{\frac{5}{6} }{\frac{5}{3} } \\\\Groups = \frac{5}{6} \times \frac{3}{5} \\\\Groups = \frac{3}{6} \\\\Groups = \frac{1}{2}[/tex]

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Answer:

Step-by-step explanation:

How do you know if side lengths form a Pythagorean triple?

Pythagorean triples may also help us to find the missing side of a right triangle faster. If two sides of a right triangle form part of a triple then we can know the value of the third side without having to calculate using the Pythagorean theorem. From the ratio, we know that it is a Pythagorean triple.

Answer:

$16

Step-by-step explanation:

[tex]0.75x = 12\\3x = 48\\x = 16[/tex]

Answer:

I think it's the second one(200(1.034)t = 250)

Step-by-step explanation:

if not correct me. or try the third one.

Answer:

173.9

Step-by-step explanation:

9.40 × 18.5 = 173.9.

Answer:

thanks for the points Imao

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

Probability of getting either heads or tails of a coin : 1/2

Probability of getting 1,2,3,4, or 6 on a dice: 5/6

Multiply those two probabilities : 1/2 * 5/6 = 5/12

You have a 5 out of 12 chances of getting heads on a coin AND any number but a 5 on a dice.

Hope this helps!

Answer:

if you download the app photomath it will help you

Step-by-step explanation:

I promise!

Step-by-step explanation:

x=27 and y= 44

.......................

Answer:

A

Step-by-step explanation:

The measure of the angle Z is equivalent to 41.7°.

Given is a right angle triangle XYZ.

Using the tangent function, we can write -

tan(Z) = XY/XZ

tan(Z) = 25/28

tan(Z) = 0.89

Z = tan⁻¹(0.89)

Z = 41.7°

Therefore, the measure of the angle Z is equivalent to 41.7°.

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Answer:

0.075

Step-by-step explanation:

3/40 = 0.075

hope it help u

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Answer:

3.5 inches

Step-by-step explanation:

create a proportion:

inches / miles = inches / miles

let 'x' = distance in inches

1/4 = x

18    252

18x = 252(1/4)

18x = 63

x = 63 / 18

x = 3.5

Answer: 4

Step-by-step explanation:

To find out how many boys are in the classroom you must divide 12 from 3 to find the rate of change. 12/3= 4 so then you multiply 1*4 to find out how many boys are in the classroom. 1*4=4

Hope this helps ;)

Answer:

4 boys

Step-by-step explanation:

3:1 is the ratio of girls to boys

Lets girls be g and boys be b

G=3

B=1

G=12     12/3=4 and what you do to one side you do to the other it is multiplied by 4 so

B=1 time 4 =4

Answer:

43

Step-by-step explanation:

65-15/5+(-19)

65-3+(-19)

62-19=43

Answer/Step-by-step explanation:

1. Sin A = opp/hyp

Opp = 3

Hyp = 5

[tex] sin(A) = \frac{3}{5} [/tex] (substitution)

[tex] sin(A) = 0.6 [/tex]

2. Sin B = opp/hyp

Opp = 4

Hyp = 5

[tex] sin(B) = \frac{4}{5} [/tex] (substitution)

[tex] sin(B) = 0.8 [/tex]

3. Cos Q = adjacent/hypotenuse

Adjacent = 12

Hypotenuse = 13

[tex] cos(Q) = \frac{12}{13} [/tex] (substitution)

[tex] cos(Q) = 0.9231 [/tex] (4 decimal places)

4. Cos S = adjacent/hypotenuse

Adjacent = 5

Hypotenuse = 13

[tex] cos(S) = \frac{5}{13} [/tex] (substitution)

[tex] cos(S) = 0.3846 [/tex] (4 decimal places)